One of the main methods of examining non-normal operators, acting on Hilbert spaces, is the theory of contractions. This area of operator theory was developed by Béla Sz.-Nagy and Ciprian Foias from the dilation theorem of Sz.-Nagy. Sz.-Nagy and Foias classi ed the contractions according to their asymptotic behaviour. They got strong structural results in the case when the contraction and its a...

Given C-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A, B-bimodule maps from B(K,H) into operator A, B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A, B-bimodules we show: if A, regarded as a Csubalgebra of Al(X) (adjointable left m...

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...

The relative commutant A∩A of a strongly self-absorbing algebra A is indistinguishable from its ultrapower A . This applies both to the case when A is the hyperfinite II1 factor and to the case when it is a strongly self-absorbing C-algebra. In the latter case we prove analogous results for l∞(A)/c0(A) and reduced powers corresponding to other filters on N. Examples of algebras with approximate...

We present and investigate a new class of quantum channels, what we call ‘universal collective rotation channels’, that includes the class of collective rotation channels as a special case. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this C∗-algebra is a core problem in a particular noiseless subsystem method of quantum error ...

Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras g of g = A2, A1 + A1, G2, and C2. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for A2 at levels ≤ 32, for G2 at levels ≤ 31, for C2 at levels ≤ 26, and for A1 + A1 at levels k1 = k2 ≤ 21. This wo...